## Interview Question

Product Analyst Interview

-New York, NY

Meta## Two points are randomly placed on a line of length 1. What is the probability that the three segments created form a triangle?

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## Interview Answers

3 Answers

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I think it might be 1/4. Lets think it in this way. We have three random numbers: a, b and c. P(a + b < c) = 1 / 2. P(a + c < b) = 1 / 2. As they are independent, the probability is 1 / 4 to meet both requirements.

Jiexun on

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1/4 is correct. This is also the probability when the second ordered statistics in u(0,1) is larger than 1/2

sha on

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I think that the answer is 1/2. The first point could be placed anywhere on the line segment and there's still the same probability of a triangle being formed. The second point is the only one that matters. No matter where the first point p1 is placed, half of the possible places that you could put p2 will not result in a triangle, because it would violate the rule that the sum of the lengths of any 2 sides must exceed the length of the third. It's easier to understand if you draw it out. P( a + b > c | a) = 1/2

Anonymous on

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